app.get('/myurl', function(req, res) {
app.post('http://some_other_domain_url_with_params?reply_url=mydomain.com/myurl', function(req, res) {});
console.log('The POST is finished. Waiting for response.');
//need separate handler for JSON response that comes back from the other domain after this
});

Your app.post call wont do a POST reqqest to another server, it is for setting up a POST route on your server. If you want to make HTTP requests to another server, it's esiest to use a library like request. Then you can use JSON.parse to turn the response JSON into a native JavaScript object.